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Archimedean Copulas in Joint Chance-Constrained Programming

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Operations Research and Enterprise Systems (ICORES 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 509))

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Abstract

We investigate the problem of linear joint probabilistic constraints with normally distributed constraints in this paper. We assume that the rows of the constraint matrix are dependent, the dependence is driven by a convenient Archimedean copula. We describe main properties of the problem, show how dependence modeled through copulas translates to the model formulation, and prove that the resulting problem is convex for a sufficiently high probability level. We further develop an approximation scheme for this class of stochastic programming problems based on second-order cone programming.

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Acknowledgements

This work was supported by the Fondation Mathématiques Jacques Hadamard, PGMO/IROE grant No. 2012-042H.

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Authors and Affiliations

  1. Laboratoire de Recherche En Informatique, Université Paris Sud – XI, Bât. 650, 91405, Orsay Cedex, France

    Michal Houda & Abdel Lisser

Authors
  1. Michal Houda
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  2. Abdel Lisser
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Correspondence to Michal Houda .

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Editors and Affiliations

  1. IMA, LISA, Angers, France

    Eric Pinson

  2. Polytechnic Institute of Setúbal, Setúbal, Portugal

    Fernando Valente

  3. Complutense University, Madrid, Spain

    Begoña Vitoriano

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Houda, M., Lisser, A. (2015). Archimedean Copulas in Joint Chance-Constrained Programming. In: Pinson, E., Valente, F., Vitoriano, B. (eds) Operations Research and Enterprise Systems. ICORES 2014. Communications in Computer and Information Science, vol 509. Springer, Cham. https://doi.org/10.1007/978-3-319-17509-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-17509-6_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17508-9

  • Online ISBN: 978-3-319-17509-6

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